To solve the given equation, we can start by using the properties of logarithms.

The given equation is:

lg(x+30.5) + lg(x-30.5) = 0

We know that the sum of logarithms is equal to the logarithm of the product of the numbers inside the logarithms. Therefore, we can rewrite the equation as:

lg((x+30.5)(x-30.5)) = 0

Now, we can rewrite the equation using the definition of logarithms:

(x+30.5)(x-30.5) = 10^0
(x+30.5)(x-30.5) = 1

Expand the left side of the equation:

x^2 - 30.5^2 = 1
x^2 - 930.25 = 1
x^2 = 931.25
x = ±√931.25

Therefore, the solutions to the given equation are x = √931.25 and x = -√931.25.